INTEGRATIVE EXAMPLE: ESTIMATING THE COST OF CAPITAL FOR DUPONT

Although a precise determination of the cost of capital is not possible, we can develop estimates that are useful in decision-making. Let’s estimate the cost of capital for E. I. Du Pont De NeMours & Company, a large U.S. chemical company whose products range from oil to pharma- ceuticals. Let’s estimate DuPont’s cost of capital for 2002, using all pub- lished ﬁnancial data through 2001.

Step 1: Determine the Proportions of Each Component of Capital If new capital is raised in the same proportions as existing capital, the

weights applied to the costs of capital would be the market value proportions of capital—the ﬁrm’s use of each source of capital, based on its market value. For example, if the market value of debt is $100 and the market value of common stock is $400, the market value proportion of debt is 20% and the market value proportion of common stock is 80%. Because many ﬁrms maintain a relatively stable capital structure, that makes it easier to determine the proportions of each capital.

THE FUNDAMENTALS OF VALUATION

EXHIBIT 11.8 Capital Structure of E. I. Du Pont Corporation, 1991–2001

Panel A Book Value Proportions

Panel B Market Value Proportions

One practical problem is determining the market value of the components of capital. The market values of publicly-traded common stock are readily available. But not all debt is publicly traded—some may be privately placed. If the ﬁrm has securities that are not publicly traded, their market values may not be available.

Du Pont has raised capital from three sources: long-term debt, preferred stock, and common stock. The debt and equity proportions, based on book values and market values, are also shown in Exhibit 11.8.

The Cost of Capital

The market value of the preferred and common stock was calcu- lated from information provided in Yahoo! Finance. The information on the market value of debt was obtained from footnotes to the annual ﬁnancial statements.

Using the market-value proportions, we see that, on average, Du Pont’s capital structure consists of 13.4% debt, 0.3% preferred stock, and 86.3% common equity. If we look at book values over the same period, we get a slightly different idea of the proportions: 32.9% debt, 1.30% preferred stock, and 65.8% common stock. If we assume Du Pont will issue new securities in proportion to its capital structure based on recent years’ market values, we expect the ﬁrm to raise capital according to the market value proportions of 13.4%, 0.3%, and 86.3%.

Comparing the book and market values, we see that the book value of common stock understates its market value. For example, at the end of 2001 the book value of equity is $14,215 million and the market value is $42,595 million. One reason for this discrepancy is that retained earnings (which typically represent a large portion of common stock) are the accumulation of earnings less any dividends paid since the beginning of the corporation’s existence. These accumulated earnings are a sum of earnings for the entire corporate life of the ﬁrm, so in Du Pont’s case, earnings in 1995 are added to earnings from, say, 1950, which are added to earnings from 1935, and so on back to 1915.

Aside from this problem, the sum of earnings reinvested in the firm do not reflect what the firm does with them when they are reinvested, whereas the market value of equity reflects this earnings growth potential.

The book value of debt understates the true value of Du Pont debt by several hundred million dollars. Most of the Du Pont debt is selling at a premium from face value—implying that the coupon rates of outstanding debt are above the current market rates. This is because interest rates are currently at lower rates than when the debt was issued.

The use of book values results in an understatement of the use of common stock—the highest cost source—and a slight understatement of the use of debt—the lowest cost source. And since the ﬁrm’s decision- makers are most likely to look at market values in assessing the ﬁrm’s current and future capital structure, it seems reasonable to focus more on the market value proportions.

Step 2: Determine the Costs of Each Source of Capital We must estimate the cost of each of DuPont’s sources of capital. To

simplify our chore, let’s ignore ﬂotation costs.

THE FUNDAMENTALS OF VALUATION

The Cost of Debt There are several ways we could estimate the cost of raising an addi-

tional dollar of new debt. We could look at:

1. Yields on recent debt offerings with similar risk.

2. Yields on recent debt offerings made by Du Pont.

3. Yields on outstanding debt of Du Pont. Du Pont debt is rated as high quality by both Moody’s and Standard

& Poor’s: Aa3 in Moody’s system, AA in Standard & Poor’s system. This means that the debt is considered high quality in terms of default risk. That is, there is little risk Du Pont will be unable to pay the prom- ised interest and principal on its current debt issues.

Using the three ways to estimate Du Pont’s cost of new debt, we obtain the following results:

1. Recent debt offerings with similar risk: For ﬁrms with Aa-rated debt that was issued late in 2001, the yield was 7.1%.

2. Recent Du Pont offerings: Du Pont did not issue debt securities in 2001. The latest issue was in mid-2000, and hence is not representative of rates at the end of 2001.

3. Outstanding Du Pont debt: At the end of 2001, the yields on Du Pont’s current debt issues were slightly lower than the coupon rates, as evi- denced by the market values being $250 million greater than the book values at the end of 2001. The coupon rates on current debt range from 6.5% to 8.5%.

Compiling these estimates we can see that there is quite a discrepancy between the rates, with estimates between 6.85% and 8.57% per year:

Approach Yield

Yield on recently issued debt of similar risk 7.1% Yield on currently outstanding debt

6.5% to 8.5% Which do we use? Which one will be enough to get investors to put

their money into new Du Pont debt? Most of Du Pont debt now consists of debentures without any sinking fund and with maturities of at least ten years. This persuades us to choose a cost on the upper end of the possible estimates. Because the debt yielding around 7% per year is more typical of the debt Du Pont issues, let’s estimate the yield on new debt to be 7%.

Though the required rate of return on new Du Pont debt is estimated to be 7%, the cost of debt to Du Pont is less since the interest on debt is

The Cost of Capital

tax deductible. Considering the tax rates on corporations for 1995, with the top marginal rate of 35%, the estimated cost of debt, r * d , is:

r * d = ( 0.07 1 0.35 – ) = 0.0455 or 4.55% per year The Cost of Preferred Stock

The cost of preferred stock can be estimated in a manner similar to that of debt. But since ﬁrms do not issue preferred stock with the same frequency as debt, it is likely that there is no recent preferred stock issue by the same company. We can, however, look at current yields on existing issues.

At the end of 2001, Du Pont had two preferred stock issues outstanding, one with a $3.50 dividend and the other with a $4.50 dividend. We can calculate the yield on the preferred stock using the current market value of the preferred stock and the dividend. From Standard & Poor’s Daily Stock Price Record, we see that the $3.50 dividend stock’s price at the end of 2001 is $59.50. Therefore the required rate of return

on this preferred stock, with P p = $59.50 and D p = $3.50, is: r

$3.50 p = ------------------ = 0.0585 or 5.85% per year

$59.50 Looking at the same source, we see that the price of the stock that

pays $4.50 per share is $74.00 at the end of 1995. Therefore the required rate of return on this preferred stock is:

r p = ------------------ $4.50 = 0.0608 or 6.08% per year

$74.00 We arrive at two estimates of the cost of preferred stock:

Approach Yield

Current yield on $3.50 dividend preferred stock 5.85% Current yield on $4.50 dividend preferred stock

6.08% Let’s use an estimate mid-way between the two current yields: 6%

per year. The Cost of Common Stock

We can estimate the cost of equity using either the DVM or an asset pricing model. An asset pricing model speciﬁes the risk factors that are believed to determine the expected return investors seek from buying a security. We discussed one such model, the capital asset pricing model

THE FUNDAMENTALS OF VALUATION

(CAPM) in Chapter 10. CAPM speciﬁes that there is only one risk factor, the overall market (i.e., market risk) that determines the expected return. Other asset pricing models that are discussed in textbooks on investment management allow for multiple risk factors. These models are called multifactor risk models. Below we will see how to estimate the cost of equity using the DVM and the CAPM. Multifactor risk models are used in the same way as the CAPM to determine the cost of equity.

Using the Dividend Valuation Model One of the key ingredients in the DVM is the growth rate of dividends. Ideally, we would like to have an estimate of the growth rate of future dividends in perpetuity. But this information is not available.

As an alternative, we look at the dividend history of Du Pont and see if the pattern of dividend payments indicates a trend. The yearly dividends per share paid over the period 1960 through 2001 are shown in Exhibit 11.9. They do not follow a constant pattern in the earlier years. But if we focus on the past few years, we get a pattern that resembles a constant dividend growth.

Du Pont paid dividends on common stock over the past four years as follows:

Year Dividends per Share

1.40 EXHIBIT 11.9 Dividends on E. I. du Pont Corporation Common Stock, 1960–2001

The Cost of Capital

We can calculate the growth rate of dividends by applying the basic valuation equation,

FV = PV(1 + r) t

Let the present value be the dividends for 1998, $1.37, and the future value of dividends be the dividends three years later, $1.40. The growth rate,

g, is the rate the dividends change each year, which is r in the basic valuation equation. Dividends have grown from $1.37 to $1.40 over three years. Therefore,

$1.40 = $1.37(1 + g) 3

And we solve this equation for the growth rate in dividends, g,

1 + g ) = --------------- $1.37

g = 3 --------------- – 1 = 0.0072or 0.72% per year

Since the most recent dividend, D 0 , is $1.40 per share, the estimate

of next period’s dividend, D 1 , is:

D 1 = $1.40(1 + 0.0072) = $1.41 The price of the stock at the end of 2001 is $42.51 per share. Substi-

tuting the known values of D 1 and P into the equation: r

e = ------------------ + 0.0072

= 0.04037 or 4.037% per year Using the Capital Asset Pricing Model To estimate the cost of equity using the

CAPM we ﬁrst need to estimate: ■ r f , the expected risk free rate of interest

■ r m , the expected return on the market ■ β, the stock’s return’s sensitivity to changes in the market’s return

THE FUNDAMENTALS OF VALUATION

We ﬁrst need an estimate of the risk-free rate that is expected in the long term. Though there are no risk-free perpetual securities, we can use the yield on a long-term government bond. Using the yield on 30-year U.S. Treasury bonds as of the end of 2001, we estimate the risk-free rate of interest to be 5% per year. 4

We also need an estimate of the expected market return in the future. The best we can do is determine a typical recent return on the market. If we assume that the market is represented well by an index, say Standard & Poor’s 500 Stock Index, we could look at the typical return on the index and use this as our best estimate of the future market return. We can estimate the return on the market by looking at the most recent year’s return, or an average market return over a broader time period. The average annual return on the S&P 500 for 30 years (1972–2001) and and 10 years (1992–2001) is:

Period Average Annual Return

We will use 11.0% as our best guess of the return on the market. Because the sensitivity of the returns on the common stock to returns on the market is speciﬁc to the individual stock, we need information on the returns on Du Pont stock. We can see this relation between the returns on Du Pont’s common stock and the returns on the market by looking at Exhibit 11.10. In this graph, each point represents

a month’s return on Du Pont common stock and a month’s return on the S&P 500 Index, representing the entire market. For example, during the month of February 1998, the return on Du Pont common stock was 8.8% and the return on the S&P 500 was 7%.

We can describe the relation between the returns on the stock and returns of the market by looking at their relation over time We do this using regression analysis, which measures the sensitivity of one variable (in our example, the returns on Du Pont stock) to changes in another (the returns on the S&P 500).

The regression of the monthly returns on Du Pont common stock against the monthly returns on the market, represented by the S&P 500, for the sixty months from January 1996 through December 2001 produces

a measure of the average relation between Du Pont stock’s returns and the returns of the market. This average is represented graphically as the regression line (see Exhibit 11.10). The slope of this line—0.54—indicates the

4 We found this rate in the Federal Reserve Bulletin.

The Cost of Capital

sensitivity—on average over the sixty months—of the returns on Du Pont stock to changes in the returns on the market and is our estimate for mar-

ket risk, beta ( 5 β). We could also obtain an estimate of β from ﬁnancial services, such as the Value Line Investment Survey. Because there are many different ways to estimate β—using different periods of time or a different market index, there may be slight differences between estimates from different ﬁnancial services. The β for Du Pont taken from Value Line is 0.95, but the beta from Yahoo! Finance is 0.7 which is close to our estimate. For purposes of this example, we will use 0.7.

Is an historical beta a good estimate of the future beta? For some stocks yes, for others no. It depends on whether the market risk of the ﬁrm is expected to change in the future.

We have gathered the following: 6

r f = 5% per year, which is 0.41667% per month r m = 11% per year, which is 0.91667% per month β = 0.70

EXHIBIT 11.10 Returns on E. I. Du Pont Corporation Common Stock versus

Returns on the S&P 500 Index, Monthly, 1996– 2001

5 The calculations necessary to estimate a regression line can be performed using a spreadsheet program, such as Microsoft’s EXCEL, or using a calculator regression

program. 6 We use returns on a monthly basis when calculating the cost of equity because we

are applying a beta estimate that is based on monthly returns.

THE FUNDAMENTALS OF VALUATION

Putting these pieces together, we ﬁnd that the cost of common stock is: r e = 0.00417 + 0.70(0.00917 − 0.00417) = 0.00767 per month

which, on an annual basis translates to:

r e = 0.00767 × 12 = 9.20%

What does this mean? It means that we expect the market as a whole to generate a return of 11% per year in the future, which is 6% above the expected risk-free rate. Our estimate suggests that investors require a return of 9.2% per year on Du Pont stock, since Du Pont stock is less risky than the market as a whole.

Reconciling the Two Estimates The different models produced different estimates for the cost of common stock:

CAPM: r e = 9.2%per year DVM: r e = 4.04% per year. This is expected since we are approaching the estimate from different

paths. The CAPM evaluates the cost assuming investors hold diversiﬁed portfolios and are only concerned about market risk. The DVM evaluates the cost assuming a particular pattern of dividends in the future. Moreover, the different approaches of these two models require us to make certain estimates along the way.

So which approach is better? The one that provides the best estimate for the cost of common stock. Which does that? It’s the model that fits our firm’s situation better than the other. To determine the better fit in the case of Du Pont, we could ask ourselves:

■ Do dividends grow at approximately a constant rate? ■ Do changes in the market return tend to explain movements in the

common stock’s returns? Du Pont’s dividends do not appear to grow at a constant rate, at least

when we look at them over a broad period, as shown in Exhibit 11.9. But Du Pont’s common stock returns do tend to be explained by movements in the market’s return. We can see this in Exhibit 11.10, where the points that represent Du Pont stock return in relation to the market’s return tend to be clustered around the regression line, telling us that the market return does explain some portion of the returns on Du Pont’s stock.

The answers to these questions—the growth in dividends and the ﬁt of the regression line—tell us to rely more heavily on the CAPM model

The Cost of Capital

in estimating the cost of equity for Du Pont rather than on the DVM model. Therefore, we will use the cost of equity from our CAPM analysis to estimate our marginal cost of capital.

Step 3: Put It All Together Using the market value weights of capital, we estimate the marginal cost

of capital for Du Pont as:

Source of Capital Weight

Marginal Cost

Weight times Cost

Debt 13.4%

Preferred stock

Common stock

Weighted average cost of capital 0.08568 or 8.568% per year We estimate the cost of capital for Du Pont to be 8.568% per year.

In other words, if Du Pont raises additional capital, we estimate that the cost of this additional capital will be 8.568% per year.

Final Considerations The calculations we made to determine the cost of capital can mislead

us into thinking that the result we obtain is precise. Rather, what we get is a ball-park estimate. Our estimate is accompanied by a number of limitations:

■ We get different estimates of the marginal cost of capital using differ-

ent costs of components. For example, we get a cost of capital of 4.115% instead of 8.568% if we use the DVM instead of the CAPM. Each model relies on different assumptions.

■ We get different estimates of the marginal cost of capital using differ-

ent weights. For example if we used book weights instead of market weights, the cost of capital is 8.6%, instead of 10.02%. 7 Also, if we look at the change in the capital structure over time, we see that Du

7 Using book value weights,

Source of Capital Weight Marginal Cost Weight times Cost

Debt 32.9%

0.01497 Preferred stock

1.3 6.00 0.00078 Common stock

65.8 9.20 0.06054 Weighted average cost of capital

THE FUNDAMENTALS OF VALUATION

Pont is using more debt in recent years, so we may wish to use a greater proportion for debt.

■ Flotation costs must be considered. We have ignored ﬂotation costs, but these could be substantial, especially if we are raising a large proportion of common equity capital.

■ Changes in costs for different levels of capital need to be considered. There may be quite a difference in the cost of capital if Du Pont raised, say $2 billion versus $20 billion in new capital.

The cost of capital of 8.568% is an estimate. With all the assumptions and judgment that go into this figure, we at least have a starting point—an estimate of the cost of capital. Knowing more about Du Pont’s target capital structure, future dividend plans, and flotation costs would help us refine our estimate, providing a more useful figure for decision-making.

INTEGRATIVE EXAMPLE: ESTIMATING THE COST OF CAPITAL FOR DUPONT